What is the length of the side BC in the triangle ABC? I. AB=8\,{cm}, AC=5\,{cm} II. Area of the triangle ABC is 10\,{cm}²

Correct Answer is : if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.

if the statement 1 alone is sufficient to answer the question.

if the statement II alone is sufficient to answer the question.

if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.

if both the statements I and II together are not sufficient to answer the question and additional data is required.

Correct Answer is : if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.

Test Index

AP ICET 2016 Paper

Question : 10 of 200

Marks: +1, -0

AB=8\,\mathrm{cm}, AC=5\,\mathrm{cm}

10\,\mathrm{cm}^2

if the statement 1 alone is sufficient to answer the question.
if the statement II alone is sufficient to answer the question.
if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.
if both the statements I and II together are not sufficient to answer the question and additional data is required.

Solution:

I. Given : AB = 8 cm, AC = 5 cm

It is not possible to determine BC. We need one more information like ∠BAC or area ΔABC or perimeter of the triangle.

∴ I alone is not sufficient.

II. Given : Area of ΔABC = 10 cm2

II alone is not sufficient.

I & II.

Using Heron’s formula, area of the triangle is given by

\sqrt{s(s-a)(s-b)(s-c)}

where

s=\frac{a+b+c}{2}

We have ‘b’ and ‘c’ from statement I and area from statement II.

Hence, ‘a’ i.e., BC can be determined using this relation.

∴ I & II together are sufficient.

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